On a semitopological polycyclic monoid
We study algebraic structure of the \(\lambda\)-polycyclic monoid \(P_{\lambda}\) and its topologizations. We show that the \(\lambda\)-polycyclic monoid for an infinite cardinal \(\lambda\geqslant 2\) has similar algebraic properties so has the polycyclic monoid \(P_n\) with finitely many \(n\geqsl...
Збережено в:
| Дата: | 2016 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/154 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| id |
oai:ojs.admjournal.luguniv.edu.ua:article-154 |
|---|---|
| record_format |
ojs |
| spelling |
oai:ojs.admjournal.luguniv.edu.ua:article-1542016-07-12T10:09:40Z On a semitopological polycyclic monoid Bardyla, Serhii Gutik, Oleg inverse semigroup, bicyclic monoid, polycyclic monoid, free monoid, semigroup of matrix units, topological semigroup, semitopological semigroup, Bohr compactification, embedding, locally compact, countably compact, feebly compact Primary 22A15, 20M18. Secondary 20M05, 22A26, 54A10, 54D30, 54D35, 54D45, 54H11 We study algebraic structure of the \(\lambda\)-polycyclic monoid \(P_{\lambda}\) and its topologizations. We show that the \(\lambda\)-polycyclic monoid for an infinite cardinal \(\lambda\geqslant 2\) has similar algebraic properties so has the polycyclic monoid \(P_n\) with finitely many \(n\geqslant 2\) generators. In particular we prove that for every infinite cardinal \(\lambda\) the polycyclic monoid \(P_{\lambda}\) is a congruence-free combinatorial \(0\)-bisimple \(0\)-\(E\)-unitary inverse semigroup. Also we show that every non-zero element \(x\) is an isolated point in \((P_{\lambda},\tau)\) for every Hausdorff topology \(\tau\) on \(P_{\lambda}\), such that \((P_{\lambda},\tau)\) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on \(P_\lambda\) is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies \(\tau\) on \(P_{\lambda}\) such that \(\left(P_{\lambda},\tau\right)\) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal \(\lambda\geqslant 2\) any continuous homomorphism from a topological semigroup \(P_\lambda\) into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains \(P_{\lambda}\) as a dense subsemigroup. Lugansk National Taras Shevchenko University 2016-07-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/154 Algebra and Discrete Mathematics; Vol 21, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/154/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2016-07-12T10:09:40Z |
| collection |
OJS |
| language |
English |
| topic |
inverse semigroup bicyclic monoid polycyclic monoid free monoid semigroup of matrix units topological semigroup semitopological semigroup Bohr compactification embedding locally compact countably compact feebly compact Primary 22A15 20M18. Secondary 20M05 22A26 54A10 54D30 54D35 54D45 54H11 |
| spellingShingle |
inverse semigroup bicyclic monoid polycyclic monoid free monoid semigroup of matrix units topological semigroup semitopological semigroup Bohr compactification embedding locally compact countably compact feebly compact Primary 22A15 20M18. Secondary 20M05 22A26 54A10 54D30 54D35 54D45 54H11 Bardyla, Serhii Gutik, Oleg On a semitopological polycyclic monoid |
| topic_facet |
inverse semigroup bicyclic monoid polycyclic monoid free monoid semigroup of matrix units topological semigroup semitopological semigroup Bohr compactification embedding locally compact countably compact feebly compact Primary 22A15 20M18. Secondary 20M05 22A26 54A10 54D30 54D35 54D45 54H11 |
| format |
Article |
| author |
Bardyla, Serhii Gutik, Oleg |
| author_facet |
Bardyla, Serhii Gutik, Oleg |
| author_sort |
Bardyla, Serhii |
| title |
On a semitopological polycyclic monoid |
| title_short |
On a semitopological polycyclic monoid |
| title_full |
On a semitopological polycyclic monoid |
| title_fullStr |
On a semitopological polycyclic monoid |
| title_full_unstemmed |
On a semitopological polycyclic monoid |
| title_sort |
on a semitopological polycyclic monoid |
| description |
We study algebraic structure of the \(\lambda\)-polycyclic monoid \(P_{\lambda}\) and its topologizations. We show that the \(\lambda\)-polycyclic monoid for an infinite cardinal \(\lambda\geqslant 2\) has similar algebraic properties so has the polycyclic monoid \(P_n\) with finitely many \(n\geqslant 2\) generators. In particular we prove that for every infinite cardinal \(\lambda\) the polycyclic monoid \(P_{\lambda}\) is a congruence-free combinatorial \(0\)-bisimple \(0\)-\(E\)-unitary inverse semigroup. Also we show that every non-zero element \(x\) is an isolated point in \((P_{\lambda},\tau)\) for every Hausdorff topology \(\tau\) on \(P_{\lambda}\), such that \((P_{\lambda},\tau)\) is a semitopological semigroup, and every locally compact Hausdorff semigroup topology on \(P_\lambda\) is discrete. The last statement extends results of the paper [33] obtaining for topological inverse graph semigroups. We describe all feebly compact topologies \(\tau\) on \(P_{\lambda}\) such that \(\left(P_{\lambda},\tau\right)\) is a semitopological semigroup and its Bohr compactification as a topological semigroup. We prove that for every cardinal \(\lambda\geqslant 2\) any continuous homomorphism from a topological semigroup \(P_\lambda\) into an arbitrary countably compact topological semigroup is annihilating and there exists no a Hausdorff feebly compact topological semigroup which contains \(P_{\lambda}\) as a dense subsemigroup. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/154 |
| work_keys_str_mv |
AT bardylaserhii onasemitopologicalpolycyclicmonoid AT gutikoleg onasemitopologicalpolycyclicmonoid |
| first_indexed |
2025-07-17T10:34:17Z |
| last_indexed |
2025-07-17T10:34:17Z |
| _version_ |
1837889967027650560 |